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Self-induced stochastic resonance (SISR) is a subtle resonance mechanismrequiring a nontrivial scaling limit between the stochastic and thedeterministic timescales of an excitable system, leading to the emergence of alimit cycle behavior which is absent without noise. All previous studies onSISR in neural systems have only considered the idealized Gaussian white noise.Moreover, these studies have ignored one electrophysiological aspect of thenerve cell: its memristive properties. In this paper, first, we show that inthe excitable regime, the asymptotic matching of the Levy timescale (thatfollows a power law, unlike Gaussian noise that follows Kramers law) and thedeterministic timescale (controlled by the singular parameter) can also inducea strong SISR. In addition, it is shown that the degree of SISR induced by Levynoise is not always higher than that of Gaussian noise. Second, we show that,for both types of noises, the two memristive properties of the neuron haveopposite effects on the degree of SISR: the stronger the feedback gainparameter that controls the modulation of the membrane potential with themagnetic flux and the weaker the feedback gain parameter that controls thesaturation of the magnetic flux, the higher the degree of SISR. Finally, weshow that, for both types of noises, the degree of SISR in the memristiveneuron is always higher than in the non-memristive neuron. Our results couldfind applications in designing neuromorphic circuits operating in noisyregimes.

Levy noise-induced self-induced stochastic resonance in a memristive neuron